An isosceles trapezoid has bases length 19 and 11 centimeters and length 13 centimeters. What is the area of the trapezoid to the nearest tenth?
what do you mean by length?
Assuming that you really mean Height for length, the area becomes
A = 13(11+19)/2
To find the area of an isosceles trapezoid, you can use the formula:
Area = (1/2) * (b₁ + b₂) * h
where b₁ and b₂ are the lengths of the bases, and h is the height of the trapezoid.
In this case, the bases have lengths 19 cm and 11 cm, and the length of the non-parallel sides is 13 cm.
The next step is to calculate the height of the trapezoid. To do this, we can use the Pythagorean theorem to find the length of the altitude.
Since the trapezoid is isosceles, we can draw an altitude from one of the non-parallel sides to the base. This forms two right triangles within the trapezoid.
The base of one of the triangles is 13 cm, and the hypotenuse is the difference between the lengths of the bases (19 cm - 11 cm = 8 cm). Using the Pythagorean theorem, we can find the height:
h = sqrt((8 cm)^2 − (13 cm)^2)
Next, we can substitute the values into the area formula:
Area = (1/2) * (19 cm + 11 cm) * h
Now, calculate the height using the formula you derived from the Pythagorean theorem, and then calculate the area using the area formula. Remember to round your answer to the nearest tenth.